Dr. Austin's Complicated (& Obsolete!) Formula

Ir = current in receiver aerial in microamperes; about 5 microamperes for a just audible signal with detectors available in 1913. On the left side of the equation.
Is = current in sending aerial in amperes. For this demonstration, this is set to 2 amperes, a common value for pack sets in 1913.
h1 & h2 = sending and receiving aerial heights in feet. Continuously variable for this demonstration by clicking and dragging the antennas up or down.
D= distance of transmission in kilometers. Either 30 or 500 Km in this demonstration.
w= wavelength in meters. Either 200 meters or 10 meters in this demonstration. Pack sets of 1913 would be more likely on 200 meters, transmitters of today on 10 meters.
e= 2.72, the natural (Napierian) base.

Some ideas back in the spark era fit the available data, but did not survive the test of time. This ugly looking formula by Dr. Austin was deduced after a long series of experiments between a shore and a ship station. The formula claims to be able to determine the signal strength at a receiving antenna based on the distance between the stations, the height of both antennas, the current in the sending station's antenna, and the wavelength in use. It predicts for instance that doubling the height of the antenna at either station will double the received signal strength. Since it was deduced using experimental data, we can assume it fit the data fairly well in 1913. From other sources for instance, we know that a ship's aerial only needed to be a few feet above the water to communicate 30 Km back to a good shore station when using 200 meters. As you can see, the formula correctly predicted that the ship's antenna needed only be 7-8 feet above the water if the shore station's antenna was 149 feet high. However, we know now that radio waves can also travel by bouncing off the ionosphere, and antenna height does not play anywhere near as prominent a role as thought back in 1913. For instance, ham radio operators conduct communications clearly and easily over distances much greater than 500 Km on 10 meters. Dr. Austin's formula predicts that such communications are not possible, since an Ir of 5 microamperes is required for a signal to be just audible. Dr. Austin's formula also suggests that 10 meters would provide a stronger signal than 200 meters at 30 Km. There was quite a bias against shorter wavelengths at the time, partly because higher frequencies were harder to produce. In time, the shorter wavelengths and skip transmission would become much more popular, and Dr. Austin's formula would become useless.
You may vary both antenna heights by clicking and dragging the antennas in this demonstration. You may choose a wavelength of either 10 or 200 meters, and a distance between the stations of either 30 Km or 500 Km by clicking on the boxes.
Adapted from an article by J. Hogan in "Electrician" for August 8, 1913.

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